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Towards a characterization of order-invariant queries over tame graphs

Published online by Cambridge University Press:  12 March 2014

Michael Benedikt  and
Luc Segoufin
Michael Benedikt
Affiliation:
University of Oxford, Department of Computer Science, Wolfson Building, Oxford, Ox1 3Qd, UK, E-mail: Michael.Benedikt@comlab.ox.ac.uk
Luc Segoufin
Affiliation:
Inria, LSV-ENS de Cachan, 61, Avenue du Président Wilson, 94235 Cachan Cedex, France, URL: http://www-rocq.inria.fr/~segoufin
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Abstract

This work deals with the expressive power of logics on finite graphs with access to an additional “arbitrary” linear order. The queries that can be expressed this way are the order-invariant queries for the logic. For the standard logics used in computer science, such as first-order logic, it is known that access to an arbitrary linear order increases the expressiveness of the logic. However, when we look at the separating examples, we find that they have satisfying models whose Gaifman Graph is complex – unbounded in valence and in treewidth. We thus explore the expressiveness of order-invariant queries over well-behaved graphs. We prove that first-order order-invariant queries over strings and trees have no additional expressiveness over first-order logic in the original signature. We also prove new upper bounds on order-invariant queries over bounded treewidth and bounded valence graphs. Our results make use of a new technique of independent interest: the application of algebraic characterizations of definability to show collapse results.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 1 , March 2009 , pp. 168 - 186
Copyright
Copyright © Association for Symbolic Logic 2009

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